You can read the original story in the Magazine here:
https://www.unz.com/PDF/PERIODICAL/StartlingStories-1952jul/69-77/

i thought if he goes closer than 5 feet to someone they will join him so he can hang out with everybody eventually

All the Time in the World was first published in the July 1952 edition of Startling Stories, which even if the month was accurate would be remarkable. In fact it's likely that the July 1952 issue was on the streets in June, the very month of the first broadcast. Of course magazines have very long lead-in times from receipt of a short story to its publication. What this means is that the tv episode wasn't actually adapted from the published story, but that the tv studio had it in advance. But from the above review it seems that if Arthur actually worked on the script to begin with, probably the whole story began as a script which after submitting it to the tv company, he then worked it into a short story and sold it to Startling.

I wonder how often this happened ... that a tv episode adapted from a short story appeared at the same time, or even before, the story's actual publication!

The climactic revelation is a newspaper stand which reads "Super Bomb Test Today". But the H-Bomb was only known as the Super Bomb to the inner circle (Teller, et al). Was Arthur letting something slip in his short story?

Esther Ralston is great in this story.

Excellent twist at the end.

Well worth watching!

Season 1, episode 37.
Original air date: 13 June 1952.
A woman proposes to rob New York`s Metropolitan Museum, using a wristwatch which accelerates time for the wearer, so their movements go undetected by anyone more than 5 feet away. The small-time crook she hires for the job doesn`t care where the artworks are going or why the woman who identifies herself only as `The Collector` wants the masterpieces.
Cast: Esther Ralston: (The Collector), Dom Hanmer (Henry Judson), Lewis Charles (Tony), Sam Locante (Bartender), Jack Warden (Steve) and Bob Williams (Narrator).
From IMDB.

esther ralston looks too tall and is too well spoken to have been a star of silent pictures during the "flapper age" . it is said that after she lost her money and she found work in sales at a new york department store she would deny her indenity to customers who remember her from her heyday. with her looks she probably just fooled herself

I hope Mr. Clarke saw this before he died.

In his "The Collected Stories of Arthur C. Clarke" he prefaces the short story thusly:

This was my first story ever to be adapted for TV - ABC, 13 June 1952.
Although I worked on the script, I have absolutely no recollection of the programme, and can't imagine how it was produced in pre-video-tape days!

The entire story is at Google Books, page 407

A small time crook is given a "shopping list"
of priceless paintings to steal and a personal
time accellerator to let him do it.

A panned photograph and a freeze-framed TV image
are used to show time stopped for everyone but him.

One quibble:
The collector in the video doesn't admit to being an alien as in the story.

Much excellant! Much much better. My cirgar and evening coffee thank you abundantly. Good job
Zigoto.